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Math Help - two calculus questions

  1. #1
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    Question two calculus questions

    Hi,

    Could you please show me how to solve these two questions? Thank you very much.

    1. Determine whether lim [sin (x^2+ y^2+z^2) ]/ sqrt(x^2+ y^2+z^2) as (x,y,z) -> (0,0,0) exists. If so, find its value.

    2. Let f(x,y) = xyln(x^2+y^2).
    Is it possible to define f(0,0) so that f will be continuous at (0,0)?
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  2. #2
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    Quote Originally Posted by littlemu View Post
    Hi,

    Could you please show me how to solve these two questions? Thank you very much.

    1. Determine whether lim [sin (x^2+ y^2+z^2) ]/ sqrt(x^2+ y^2+z^2) as (x,y,z) -> (0,0,0) exists. If so, find its value....
    Hi, ,

    I've attached my calculations:
    Attached Thumbnails Attached Thumbnails two calculus questions-dreid_limit.gif  
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  3. #3
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    Quote Originally Posted by littlemu View Post
    Hi,

    Could you please show me how to solve these two questions? Thank you very much....

    2. Let f(x,y) = xyln(x^2+y^2).
    Is it possible to define f(0,0) so that f will be continuous at (0,0)?
    Hi,

    I've attached the calculations and the graph of the function:
    Attached Thumbnails Attached Thumbnails two calculus questions-dreid_funccalculations.gif  
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